D-R143 647 THE CALCULATION OF THE RADAR VERTICAL COVERAGE DIAGRAM 1/1(U) ROYAL AUSTRALIAN NAVY RESEARCH LAB EDGECLIFFM R BATTAGLIA MAY 84 RANRL-T/NOTE(EXT)-1i84
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DEPARTMENT OF DEFENCE
DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION
R.A.N. RESEARCH LABORATORY
EDGECLIFF, N.S.W.
RANRL TECHNICAL NOTE
(External) No 1/811
THE CALCULATION OF THE RADAR VERTICALCOVERAGE DIAGRAM
M.R.BATTAGLIA -CT "
THE UNITED STATES NATIONALTECHNICAL INFORMATION SERVICE
IS AUTHORISED TO
REPRODUCE AND SELL THIS REPORT
C=3 APPROVED FOR PUBLIC RELEASE
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. No. May 1984
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UNCLASSIFIED
DEPARTMENT OF DEFENCE
R.A.N. RESEARCH LABORATORY
(E Commonwealth of Australia (1984)
RANRL TECHNICAL NOTE (EXTERNAL) No 1/84
THE CALCULATION OF THE RADAR
VERTICAL COVERAGE DIAGRAM
Accession For
N4TIS GRA&IDTIC TAB
M.R.BATTAGLIA UnannouncedJustification
By-
00. Availability CodesAvail and/or
Dist Special
AN0
ABSTRACT
Algorithms are described for the calculation and plotting of radarvertical coverage diagrams. Two contour VCD algorithms are presented, witha brief discussion on the problem of numerical stability, and the effectsof ship motion and frequency agility.
POSTAL ADDRESS: The Director, RAN Research LaboratoryP.O. Box 706 Darlinghurst, N.S.W. 2010
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4 CONTENTS
1 o INT~RODUCTION 1
2. THE RADAR EQUATION 1
3. REQUIRED SIGNAL-TO-NOISE 2
3.1 Approximate Formulae 2
3.2 Iterative Solutions 4
4. THE RADAR VCD 4
4.1 VCD Envelope 5
4.2 The Roughness Factor 6
4.3 Antenna Pattern Functions 7
S. GRAPHICAL REPRESENTATION OF VCD 7
6. CONTOUR PLOTTING 8
6.1 Asymptotic Behaviour - The flat Earth Limit 8
6.2 Spherical Earth Model 9
6.3 Description of Main Program 10
7. EFFECT OF SHIP MOTION 12
8. FREQUENCY AGILITY AND DIVERSITY 14
ACKNOWLEDGEMENTS 14
REFERENCES 15
LIST OF ANNEXES
A Calculation of Threshold for Fixed Threshold Detectors 16
B Calculation of Paint Probability for Marcum, Swerling
and Veinstook Targets 17
C Calculation of Required Signal-to-Noise 18
D Calculation of Paint Probability for Non-fluctuating Targets 19
E Main Program for Contour VCD Calculations 20
DISTRIBUTION 42
DOCUMENT CONTROL DATA SHEEr 43
1. Introduction
Operational performance of Naval radars is routinely checked by
measurement of the vertical coverage diagram (VCD). Comparisons of returns
from a calibrated target with the VCD facilitates the detection of any
degradation. This may be in the form of a lower average detection range
or 'holes' in the vertical coverage. The former may result from
electronic degradation or transmission line losses, while the latter may
result from antenna damage or multipath effects - these being determined
by sea state and choice of antenna height or operating frequency.
In reference 1. computer programs were described which calculated
(i) the radar return from a target flying a specified height/range
profile and (ii) the probability of paint for fluctuating and non-
fluctuating targets. Refinements to the model, and the theoretical basis
of the algorithms were outlined in reference 2.
Comparisons have been made between the output of these programs
and the measured returns in the RAN sphere drop calibration trials. In
the absence of ducting, any differences can generally be attributed to
plumbing or other isotropic losses.
RANRL has been requested ( ref 3 ) to produce programs suitable
for desktop computers to solve the inverse problems - (i) the calculation
of signal-to-noise required to yield a given probability of paint and
(ii) the calculation and plotting of detection contours in a multipath
environment. The ensuing sections describe the algorithms used in the
programs.
2. The Radar Equation
The power returned in free space from a target of cross-section .
is given by the monostatic radar equation
Pr= PG 5 1.GX"
where Pt is the transmitted power, G is the power gain, X is the radar
wavelength and R is the target range. Multipath, diffraction and other
environmental effects are accounted for by the pattern propagation factor
(F) and the atmospheric loss factor (L)
Pr = P GS'SfF4 2.(4ruR4,
2
The problem aderessed in this paper -;' the calculation of L.in equatic-n
2, which may toe recast to provide ar, eipiession for the mrximur, -.itgle-bllp
detection range:
Ra = L(4r; oLIs F 3.
wbere Pt is the peak tiansmitteC power vnd Pn is tbe systen. noise
power. Do is the single-pulse signal-to-noise ratio requiied to yiele
the eesired probability of paint for a given numbe2 ci pulses "nttgiated,
false alarm rate and target itturt, statistics. In tht abserce of clv:ter,
the limit to signal detectability is goveired by the pulse energ, so that
the effective noise po%cr P. referred to the artvna, is determrined by
the tionsmitted pulse width (z), the antenna ncist. tenpeiature (Ta), the
receiving line IcLses (L) and the receiver noise figure (N)
Pn = k/ [Ta + Tr(Lr-l) - LrTo(N-I)] 4.
where Tr and T c are the tecipei-uture of the receiving line and 290 K
rtspectively, and k is Boltzrann's constant. If the receiver noise band-
width En is used instead of 1/v in (4) the transmitted power should be
nultiplied by Be, the time-bandwieth constant, to give the effectiv. S/lN
for probability of detection calculations. If clutter-to-noise is near
unity, it is convenient to, assume that the clutter-plus-ncise vatiable
(PC +Pn) has the same statistical distribution as ieceiver noise, and this
Rayleigh distributed total noise power is tsed for Pn in equation 3.
3. F.equired Signal-to-Fcise
3.1 Approximate Formulae
There are numerous approximate formulae in the iadax 'iterL.ttre
for evaluating paint probabilit) from S/F (and .ice versa). Reasouable
estimates of eetection range can be obtained using the simple forrila
suggested by Neuvy ( ref 4 ):
D = 10 log [a log i PFA l0 NY (Iog(I/Pd)
where PFA is the probability of false alarm, Pd is the probability of
paint, V is the number of pulses incoherently integrated. The detector
law is described by the 'constant' y which is often given the empirical
value of 2/3 ( ret 5 ) rather than the asymptotic limit of 1/2. Neuvy
has given heuristic estimates of a and A for the Swerling and Varcum
(non-fluctuating) targets as shown in Table 1.
3
Swerling 1I 2/3[1 + 2/3 exp(-N/3)]I I I
II I I 1/6 + exp(-N/3) I111 3/4(1 4 2/3 exp(--N/3)]1 2/3
IV 1 I 1/6 + 2/3 exp(--N,/3) IJ___ Non--f1uc tuatirg_j .. . . 1_ _ _ p _p rt f _ __j ------- 6. .. . ... ..._I.-
Table 1. Neuvy parameters for Karcum and Swerling targets.
Sweiling Case
N I lII 11 1V Eqr. (6)
1 10.5924 10.3747 10.5924 10.3747 10.5924
2 8.1681 7.9547 7.9547 7.9295 7.9547
3 6.8091 6.5984 6.5735 6.5938 6.7176
4 5.8732 5.6644 5.6443 5.6807 5.60605 5.1639 4.9565 4.9478 4.9907 4.8528
6 4.5949 4.3888 4.3926 4.4380 4.2808
7 4.1213 3.9163 3.9320 3.9781 3.818F
8 3.7165 3.5123 3.5392 3.5851 3.4310
9 3.3636 3.1601 3.1972 3.2425 3.0968
10 3.0511 2.8483 2.8947 2.9391 2 8030
20 1.0674 0.8689 0.9763 1.0105 0.956030 -0.0397 -0.2360 -0.0962 -0.0687 -0.0798
40 -0.8042 -0.9989 -0.8384 -0.8153 -0.8024
50 -1.3861 -1.5798 -1.4045 -1.3845 -2.3574
60 -1.8550 -2.0479 -1.8613 -1.8437 -1.8079 14
70 -2.2471 -2.4393 -2.2438 -2.2280 -2.1871
80 -2.5837 -2.7754 -2,5726 -2.5583 -2.5143
90 -2.8785 -3.0697 -2.8608 -2.8476 -2.8021
100 -3.1405 -3.3312 -3.1171 -3.1049 -3.0590
200 -4.8285 -5.0169 -4.7736 -4.7666 -4.7370 R
300 -5.7918 -5.9791 -5.7225 -5.7175 -5.7111
400 -6.4664 -6.6531 -6.3883 -6.3844 -6.3996
500 -6.9853 -7.1715 -6.9012 -6.8980 -6.9324 "
600 -7.4065 -7.5925 -7.3180 -7.3153 -7.3670
700 -7.7611 -7.9467 -7.6691 -7.6667 -7.7340
800 -8.0672 -8.2526 -7.9723 -7.9702 -8.0516 17
Table 2. Required signal-to-noise (dB) tabulated for N=I to
800 pulses integrated (PFA=0.000001, Pd=0.3 3 ).
Iterative solutions (columns 2-5) used fitted data
in column 6 as 'first guess'.
-------------------------------------------------------------
These formulae are accurate to %ithin a few dE for C.I<Pd<0. 9 and mod-
erate values of N. This rarge is not adctuatt ,ircc (i) the 95% contour is
often srecif-cd as the requiied detectability contour and (ii) cumulative
paint piobability considerrticns ,ithit waiiant the plotting of a Pd<105
contoLi. The fornLlae also do nct give good agrecvert for 1<N<5 whict. is
typical for 3-D radar, nor are they applicable to vei3 slowl, fluctuating
(Weinstock) targets. Expressions of coripaiable acctracy hare beer given
by Albershein. (ref () and Blake (ref 7) for r.cn-fluctatirg taiget,.
3.2 Iterative Sciutions
The formulae described above ri. x(t valic over a sbfficientl.
large range of Pd' N, PFA and target scintillation rate to be hsed for
routine VCD calculations, but are sometives useful in providing a staiting
point for an iterative algorithr. Hovievcr, in the unreliable regions
(such as modexatel large F" and Fd>90. ) numerical instrbility poses a
serious problem. A more robust startling point is required which covers
the range of zaday Erd target parameters likely to be crcacurtexed.
The rtuthod used here is based on the observation that Do, for 33%
probability of detecticn in gaussian noise, is virtually independent of
the amplitude statistics of the target ( see figure 1 ). Regression
analysis of Do data for PC,=0.33, 3<N<1000 , PFA=10 6 , Swerling case II,
and non-cohelrent integration yields the following result
Do = 7.138 + 1.018/log(N) - 5.533.log(N) 6.
with DO in dB. Values for N=1 and 2 are evaluated separately in the
program.
The secant iterative method with equation 6 as first guess,
together with the algorithms of reference 2, were used to produce the
data in table 2. Iteration was stopped at Pd = 0.33+0.00001. The
accvracy of equation ( is of the order of the dependence on target
scintillation ( ±0.1 dB ) at 331, probability of detecticn. Results for
505 and 95% (+ 0.001%) are shown in graphical form in figures 2 and 3.
4. The Fadar VCD P
In free space,the detectability contour, or vertical coverage
diagram, is deterrined by equation 3 with F replaced by the antenna pattern
function f(O)I
Rmax = f(O).R o 7.
where Ro is the detection rarge along boresight, and 0 is the elevation -A
-y . rb *. .- .-- .
angle. This smoothed contour is also useful lot estimating mea, ectectija
ranges at higher elevation angles and modeiate sea states, in which case
the multipatb structture is washed out (see also latei section on ship
motion). At lower elevation arigles. or sea states, multipath lobing mu.t
be considered and the detection ccntcx becomes
F.f.ax = F.F0 ..
Un'4er ncn-ducting conditions, the pattern propagaticn -actor, F in, the
interference region is
F = f(O1 )./1 + x2 + 2x cos 0 9.
and may take values between 0 and 2. The phase diffeience 0 is tht sun of
contributions fjom the geometric path difference betveen the direct ar.d
indirect rays ( fig 4 ), and the phase difference cn xcflecticr frotn tLe
sea surface of the indirect ray. The reflectixity paraveter , is
X . r p D f(e2 ) 10.f(O1)
in which D is the divergence factoi, j is the roughness factor, p is the
dielectric reflectisity (tie reflectisity which would apply if the sea
were perfectly s.'octl,) and 0, and 02 are as shown irn figure 4.
For elevation angles near the horizon, and for targets over the
horizon, F is calculated using diffraction theory (or by interpolation as
described in ref 1) with
F--- f( 1 ).'U(X).V(Z1).V(Z2 )
where X, Z1 , Z2 are range, target height and antenna height respectively
in natural units and the functions V and U are gain functions described
in refeer,ce 2.
4.1 VCD Envelcpe
The main features of the VCD for Naval radars can be calctlArted
using ray theory. The envelope of Fdna, is obtained with equations 6
and 9 with
0ma = 2fm ( m=1.2,3 ...... ) 12.
so that,
RMa(envelope) f( 1).(14z).R O 13.
C61 . . . . .*~ .< .
6
Within the range of elevation atC grazing angles of interest,
the shape of the VCD is thus dominated by f(O) and r.
4.2 The Roughness Factor
The reflecti~ity of the indirect ray can be written as
r = r.p.e -A 14.
where r is the roughness factor, and p and 0 are the magnitude and
phase respectively cf the speculai reflection coefficient. Formulae
for p and 0 as functions of grazing argle, frequency, water tempeyeturt
and salinity are given it reference 2 and are in good agreement with
experimental data. The dependence of the roughness factor on gie~irg
angle and frequency is less straightforward, and tler( is a pa~city (,f
experimental data.
Ament ( ref 8) has shown that if the wave height distribution
is gaussian, (variance a2 ), then the surface roughness will slso be
gaussian
r = e - 2 s 2 15.
where
s 27ray.siny/k 15a.
This equation gives good agreement at low giazing angles (y),
but this is to be expected since r--)l as y-->O. That is. most models
will predict r-'ax~2Ro for the lowest a-ultipath maximum over a wide range
of frequencies and sea states, despite the lack of agreement for the high P
altitude coverage.
At higher values of s the reflection is net purely specular. The
additional diffuse component adds to the fluctuation in the pattern
propagation factor, but act to its average value. The randor, corppoent
of F is not considered in the program, but rather an effective constant
value is assumed. Reasonable agreement for large s is obtained using
the empirical expression given in reference 1:
r = e- 2 s2 for r00.44 16.
= e- 1 "2732s r(=0.44 AThe program also makes use of the Burling relationship between ,
significant wave height (E1/3 )and a
r1 13 M 4 17.
.j I'
7
4.3 Antenna Pattern Functions
At high elevation atgles and nricdeatt sea states x-- >0 and tl,e
envelope of F is dominated by ttl APIF, as per eqn 7. Flsewhere, themax g
antenna patterr function of botb the direct at;d irdiiect rays a e
required for the calculation of F. In L.eeral, the APF nees te 1,e
represented adequately out to the first sidlobe. The lcgran calculatus
either (i) a cosecant-squared pattern oi (ii) a rodified sir uiv far bean.
of tle form
sin rrfYt- BI U.f(O) ir-T
where u:-d.sinO/X aild B is a constant fcr the antenna which dcrxibes tbL
sidelobe level and apeiture efficiency. ?!tbods for calculating F fron
the sidelobe level are described ir zefeierce 2
5. Ciaphical Representation cf VCD
In the abserce of ritcb and iol the VCD is indepcident of radqx
azinutl (neglecting blind arcs and supcistrrcttiv multipath) so that tiC
VCD can be displayed as a 2-D graphical represer tation. Variations uitl,
range and height of paint. probability or signal-to-noise can be
escribed by an arbitrary numbei of grey scales
In figures 5-8, the VCE' of a i11F air search radar and a G-band
surface search radai are illustrated for two sea states. Gross
parameters used for the I1IF radar are k - 0.7 metre, antenna height hI
30 wetre, N-75 pulses incoherently integrated, sea states 0 and 6. and a
free space rarge of 10 r 80 n.miles agairst. a 1 metre-squared target.
Parameters used for the G-band radar are X - 0.05 metre, h1 = 25 metre, N
5, sea states 0 and 3 and I) 17 n.miles. Standard atmospheric
conditions and scan-to-scan (Sweiling case I ) target scintillation are
assumed. The grey scales correspond to paint probability regions P>95%,
50%(P(95%, 5%,(P<50T and P<5%, and seie computed as described in the *
previous section.
The V'CD's were produced by taking 120 cuts in. height fer 200 range
increments. Sea clutter was ir-uded ir the noise calculaticns, using 6
the expressions described in reference 2 For reasons cf clarity the
plots are not truncated at winimum iange arid r..axitiur t-nacbiguous, iange as
determined by the radiated pulse width and PRF respectiel3. In order to "
resolve the structure in the G--bad plots, calculations ve.e carried out %
only to 4000 feet and limited to sea state 3, while the fliF calculations
K _________
were carried out to a height sufficient to contain the 55A probabiIity
ccntour.
The calculations for figures 5-8 took a few minutes ol pzocessirg
time on a CDC Cyber 76 mainfrone ccmpauter. Such a progran is howcvtx
Lusuitable for small desktops, such as the Tektronix Graphics System
specified in refererce 3, since s'ni]ar calculations viculd take 2-3 days
of computer time for each plot. The next section describes methods for
producing live contour VCD s which can be quickl3 computed on a .v-all
desktop roachine, using a nrodificat.c.n of the prograL descxibeo, ir. ef I'
6. Contour Plotting
6.1 Asymptotic Behaviour The Fiat Eartb Limit
Fast algorithms for computing contour NCD s aic nct easily
implerented due to the 'ack of -. ,ieti3 it: the ruit iath lob!Ig
structure. One method often employed i t to perfoin, an approxiat e
calculaticn of the VCD using the flat earth mrtltipatb iesults anid to modify
the computed results graphically or by scalinE to account fox cuisatvue
Ever this approach howevei Yill not be generally applicable due to the
additiona! georetric approximations ti-at nmust be made
In the flat earth limit D: 1 and, for horizontally polarized UlHF
iadais at low to modexotc elevaticr angles. r=l and the phase difference
Cn reflection is n. r adians The path d~fference between direct and
indirect rays for a target at ground range G is
f= (h1 4h2 )2 + G -62 (h2 -h1 )2
G2
If the frce space range of the iadar is large conzraied with the
sum of target and antenna heights the path difference for ccnstxuct e
interference is given approxin:ate!y as
- 2h 1 h 2
R cosO
Voithin the antenna main lobe (f(O)-l) the pattern propagation
factor then simplifies as%
F =2 sin(2nhlh 2 /XG)"
2 1 sin 2nh (tanO h 20.x20.
9
Usually C>>hl/tanO for r.aval searcb radars at ranges of irtelest,
so that the VCD's produced fi(,v the fp"t earth mudel are highly symmetric
- that is, only one rai;uiation of a-ultipatb geometiz ned be perfir,td
for onr lange at each elevation anglt ircrement, vith F.- scalinrg t.
deternine the range for a specified probability of detection and false
alarm rate (using the algorithms of section 3). A first order ccrrect in
for the effect of the earth's curvature car Le incjvded afttr the last
approxivation. This is equivalcrt tv as,:t.ing that the s.ca surface is
fl-t up to the point of reflectin so that the final reslit xecui es cnl
the tiansforation h2 -->h2 4 G2/2a e .
The algorithr,:s used ir the progran described here do net rely on the
flat f:th model, however the gross structure of the VCP can be detenrired
using the procedure described above. Suc, a descrirticn is therefort, a
useful basis foi a more general algorithm.
6.2 Spherical Earth Yodel
- Dependence of F on Lange
The flat earth model pxecicts that the lobe maxima for long range
naval radars occur (with F=2 ) ut elevation angles
e sin-1(2m-l)X/4h I m-1,2,3 ..... 21.
It is clear from figures 5-6 that, in the more general model, F-2 at th. lobe
maxima only at low elevation argles. This implies, not only that twice the
fre space range will be achieved only at lower altitude, but also ti-,st the
lobe sacirg is not uniform. Equation 21 is, however, useful for dett'inining
the elevation angle spacing zequired tc fully resolve themultirath stricture.
In the prograr, ten poir.ts axe calculated per nominal lobe spacirg. This
facilitates both resolution of the lobes and the ability tc read tb radar
rarge fro'w the plots to a within a few percent of L•
..
The behaviour at ccrstant elevation angle for a spherical earth
is most easily demonstrated graphicall. Figures 9 and 10 are typical
plots of the signal return fox the UHlF radar desci ibed in the prelious
section. The plots axe for a 1 metre-squared target at two internediate
elevation angles, separated by half a nominal lobe spacing, at sea states
0 and 6. If the free space range of the radar is large corpaved with the %
clutter horizon, algorithrE for contour VCD s are likely to be most
stable at higher sea states due to the reduced multipath lobirg. This is
seen in the plot fox sea state 6 (figure 10) where results for both
elevation angles yield results which are close to the free space result.
Since the powex retutrn decays as tht fourth power of xanCe, either a
scaling or iterative algorithm should calculate the required .
10
signal-to-noise in one or two iterations even if the first
inaccurate.
The behaviour at low sea states is less well b
robust algorithas are generally xequred. In figure 9 t
at the free space range (80 n.nwiles) is qualitatively di
two elevation angles selected. One curve corresponds 1of a lobe maximunr (at 80 n.triles) and R- 4 behavicur is s
2.0 times the free space range. This type cf bel.axiour i.
and implies that as long av the first guess for lcng
around the free space rarge, the Cdetection range (S/N=E o0
trazira will generally be easily conputed. At very shc
hopping occurs for constant elevaticn angle calculations s4
algoiithnms may be numerically unstable.
As a corollary, iterative algorithms nay be uns
Srange search radrars such as the G-band radar of the rievic
the worst case there may be either no solution or fevera
S/N=F 0at a given elevation angle. The formei case may ap
sea states if the detecticn range is of the order of the c
%hile the lattcr will be worst at low sea states wbei(
lobing is most pronounced.
6.3 Description of Yain Progran
Either of two algorithms vay be selected in the na
cases where iun-erical stability is not a problem the pref
calculaticn is an iterative search method. This algorit
reliable results at moderate sea states for naval radars
is large compared with the clutter horizon. This method
there is a solution along a selected elevation angle and
is reasonable (power monotonically decreasing with ra
detection range can be calculated with arbitrary preci
sensitivity of C.25 dB should be acceptable for most app
10 points are plotted per nominal lobe spacing.
In order to increase the probability of the searc
numerically stable region, the first two corrections to tf
aie scaled assIVirg R- 4 and F.-I decay law respectively
reduce ringing), %ith subsequent iterations independent ol
If a solution has not teen obtained by a specified number
the 'solution' plotted will correspond to the ainimum val
Ttis nicthod will therefore produce reliable ranges in
structure but net necessarily in the nulls. This loss of
of little cor sequence (see figures 5-8) cspecially considt ring that the
power in the nulls is highly va iable due to ship mauticn (discussed in
next section) , wave height fluct Laticns, strosheric inhotogereity, and
other factors.
The second algorithm is a one--step scaling algorithr, so that the
Computee detvctability range, at a specifitd elevaticn aiglc, will in
general be reliable only if the first guess is close to the actual
detectability range. The scaling algorithm in the peograa is optimized
to produce a reliable envelope for VCD contour since the first guess at
any elevation aiL.le is the range to the lobe maxi.urn, gixen by equation 13.
Since the ref'ectivity parareter x is a function of R, it is not known until
the final solution is obtaired. An estimate x is used, and this provides .
an estimate -:
~ax0Rmx= Ro f(O). (I+'i) 22. .
The estimate Ni is the value corresponding to the last solution
(xiil). With this procedure, Rmax will be calculable to within a few
percent at sea state 0 if at least 10 points are calculated per multipath
lobe. At higher elevation angles and/or sea states the multipath lobing
structure is wasbed out (xi-->O) so that this algorithm will be both
robust and accurate if R.o is greater than the clutter horizon.0
Plots using these algorithms are given in plots 11-17. The
contour selected is C dB in all cases, which corresponds to 4% and 52%
probability of paint for the G-band (N=5) and UHF (N=75) radars
respectively against a Swerling case I, I metre-squared target
Figures 11 and 12 used the iterative algorithm (0.25 dF sensitivity) at
sea states 0 and 6. The contour VCD's are in good agreement with the
grey scale envelopes of figures 5 and 6. An additional plot for sea state
3 (fig 13) is included to illustrate the gradual, and ver) significant,
decrease in maximum height sith sea state. The same parameters were used
to produce the plots in figures 14 and 15 with the scaling algorithm.
Although this algorithm is optimized at the lobe maxima, it also gives
good agreement in the mid-lobe region. The lower half of each lobe is
generally well reproduced to much shorter ranges - this is fortuitous
since this is the lobe region of interest for inbound air targets.
Figure 16 and 17 show the results of the scaling algorithm for
the G-band contours, with the calculations stopped at an. elevation angle
corresponding to the maximum height in the full graphical representations
(fig 7-8). Again, the 0 dB contour (4%) is consistent with the 5% grey
12
scale envelope of figures 7-8. With t. is radar, the patterrn propagation
factor has a stronger range-dependcice Fc that the iterati e algorithm is
numerically less stable. The mail lesta:ion cf tiis is a VCD) with a much
higher incidence of 'baC' date pci,,ts (abcut 5% of all points calculated).
At sea state 0, the lobes for this radar are pronounced but closely spaced
so that only the envelope of the VCI) contour is easily measured (sifticient
reascn for using the quicker scaling rmcthd). At hilher sca states the
effect of ship moticn further complicates the VCD.
7. Effect cf Ship Motion
The motion of the ship is most coxverientl3 described in tcrns of
the reference axes systems defined in figure 18. A natvrel choice for
the 'space-fixed' axis system utilizes the mean sea surface as the x-y
plane. The ship's axis system is also naturally defined by the effective
plane of symmetr) through the keel, which is defined as the x'-z' plane,
with the y'-axis passing through the antenna.
Relative motion of the two axes systems about the vertical (yaw)
is equivalent to a fluctuation in the antenna rotation rate and, thus,
the number of pulses integrated. Similarly, the number of hits per scan
is increased or decreased during a rapid turn. Although this motion may
be of the same order as the normal antenna moticn, the probability of
detection is only a weak function of the number of pulses incoherently
integrated, and can therefore be ignored in most cases. Motion of the
ship in the x-y plane is also ignored since the VCD is plotted in terms
of relative range which will not change significantly during the time on
target for norrral antenna rotation rates and target range rates.
Pitch and roll can be defined as the angles 0 and 0
respectively in figure 18. The effects of ship 'rotation' are symmetric
ir pitch and roll unless a specific target bearing is considered. For a
target on the bow, pitch has the same effect as varying the antenna tilt
in the x,y,z axis system while preserving the polarization of the
radiation. (The effect of the vertical motion of the antenna during
pitch/roll is discussed later in the section on heave). Pitch or roll
can be significant compared with vertical beamwidth, even for wide
beamwidtb search radars. This not only has the effect of increasing the
maximum angle of the main antenna lobe VCD, but also gives rise to
calculable fluctuations in the pattern propagation factor at. moderate
elevation angles due to variations in the APF of the direct and indirect
13
rays. This is shown in figure 19. where the antenna tilt was allcwcd to
Nary randoirly between zerc and 1i1)% c, " th vertical beamwidth.
The effect of roll for a '"rTet along ztc, relative bearirg also
has a small a-zirrutt f1ucteizi i, 4ftett for taigt-ts at t-odexate elevation
angles. (This effect is not nc, aYally sitnrificant, or else it would
provide an elegant method of detcrnu ir ing taigett elevati cr usirg a 2-D
% " radar.) A second effect for this relati;( geometry is that polarizaticn
of the radiation in the space-fixed system is pa.,tially converted to the
opposite sense. The detect ing ant etaia "s enly corce rned %i th tie polar iz-
ation in the ship's axis system, so that this is on.) wanifested tbrough
rultipath effects. Six degrees of roll converts only 1% of the radiatiorn
to the opposite polarizaticn. At grazing ircidence foa the indirect ia%,
the phase difference and reflectivity are near n and I respectively for
both polarizations, so that the lowest lobe is virtuali independent of
polarization. At moderate elevation, the ragnitude and phase fcr vertical
polarization may be sufficiently different to put maxima at the elevation
angle of a minirmum for the opposite polarization. Since the detection
range is of the order of (SiN)O. 1 , the nulls for a 1% polarization
change way be filled to about a third of the range for the adjacent lobe
maxima.
In the case of heasc, the effect is simpl. related to the ratio
of heave to mean entenna height above sea level. A simulation of the
effect of heave is shown in figure 20 (one run only),where the antenna
height was uniformly distritwed over the nominal heave dimension. The
effect on the lower lobes is only slight, but heave has the effect of
filling in the upper lobes and thus reducing the mean detection range
along a lobe maximum. If the meai, of many simulation runs is calcrlated
for each elevation angle, the nulls at the n-th lobe will be completely
filled if n is of order (antenna beigbt/2.heave) or greater, decreasirg
in effect with decreasing elevation angle.
Ship heave will also affect the probability of detection by its
effect on the target fluctuation statistics. In the case of slowly
fluctuating (Weinstock) targets, hz.nve will modify the scintillation to
scan-to-scan (Swerling case I) at higher elevation angles but will have a
reduced effect on the amplitude statistics at lower argles. Targets with
Suerling case I-IV statistics will not be affected to the same extent
since ship motion is negligible on a pulse-to-pulse timescale for typical
PRF's.
Va- 7 74 7 7.7I..:w 5
14
8. Frequenc, Agilit% and biversity
N ~The rada is LtiS~ios ed alt- e ad_: assumned to have a transwittted
frequency bandwidth of er~lci C~c t>5' eCF tic pulscwidth - typically
1 MHz. With pulse com~pression -i a it is tihe inverse of the compressed
pulsewidth. In adidit ion. tne r!ie -ref-iecy ma': be tuned ov'er a range
of several percenit -- rygi(,a1y trns c,; Miliz. The Eingie-pulse bandwidth
is small compart-C with the ;evtj-c trequericy, an ' so as no significant
affect on the VCU, while the tuiability of the catdai set simpil cbenges
the number of lobes ti-at f i if.to the arcenna in luIbe at fairly long
time irtervals. (The frequecoci tcrm ti: the radai. equation caz' be assumed
to be a constant, sinck the detect iorn range varies as the square root of
the wavelength.)
Frcquenicy agility has an analogous tffect on the radai. VCD. Th e
detectability, averaged over all tiaujsmitted frequencies, m~ay be the same
as a sirple tunable radar, however o-, a se.an-to-scan t imescale the radar
VCD's are quite different. The elevation angle to the n-tb lobe is
approximately proportional to the ratio of the transmitted wavcltngtb to
the antenna height. If the agility was random, and ona a scan-to-scan
basis, the effect on the VCI) would be similar to the heave siniulation in
figure 20. That is, the lower lobes would be unaffected but the power in
the upper lobes would be fluctvating atcut the free space level. Pulse-
to-pulse random agility yields the samie mean detection range but the
fluctuations are averaged out in the integraltien process. A second
effect of random pulse-to--pulse frequency agility is on the number of
irdependeptly fading signal groups per scan, or alternaEtely the number cf
degrees of freedom of the eqluivalent Chi--squa rc t arget . If F frequencies
are transmitted per scan with sufficient separation to have independent
echoes, then a target which is represented as having 2K degrees of
freedom for the fixed frequercy radai ba~s up to MKI degrees of freedom
for the pulse-to-pulse frequency agile radar (K=F,N,2F and 2N for
Swerling cases 1,11 111 and IV respectively )
Acknowledgement.
Helpful suggcstiorts from Lt~dr P Williams are acknowledged.
S. . . . . .. . . ..
:.'. 15
p..
1. Battaglia, N.R. (1983). RAN Research Laboratory. A Coaputer Program
Afor the Prediction of Search Radar Performance. (U)
IRANRL Tech Note (Ext) 1/83. UNCLASSIFIED.
2. Battaglia, IA.R. and P.Williams (1983). RAN Repearch Laboratory.
A Model of Radar Propagation and Letection.(U) 1ANRL
Tech Note (Ext) 2/83. UNCLASSIFIED.
3. RANTAU Vinute 59-17-2 (DS) , 7th Sept 1983 (R).
4. Neuvy,J. (1970) 'An Aspect of retermining the Range of Radar ltetection',
..F..E.F. Trans on Aerospace and Electronic Systems, AES-6 (4),
p 514.
5. Brookner,E (Ed) (1977) .RadarTchnolSy, Artech, Dedhaw, p 387.
6. Tufts, D.W. and A.J.Cann (1983). 'On Albersheir's Detection Equation',
I.E.F.E. Trans on Aerospace and Electronic Systems, AES-19 (4)
p 643.
7. Blake, L.V. (1980). Radar Eange Performance Analysis, D.C.Heath
and Co., Lexington.
8. Ament, W.S. (1953). 'Toward a Theory of Reflection by a Rough Surface',
Proc. I.R.E., 41(1), p 142.
".
4.
16
AYNEX A
Calculation of Detecticn ThresholdFor Fixed Threshold Detectors
1201 REN **************** * * ******* ****i**********- 1205 REM UTILITY ROUTINE TO CALC SUM NO:0 TO N-I OF YOM.e^-YO/MI
1206 DEF FN LGT(X)=LOG(X)/LOG(10)1210 IF N>1 GOTO 12151211 Y2=EXP(-YO)1212 RATIO=1.01213 GOTO 12801215 NO=0:ANSWER=0
' 1216 LIMIT=1.0E351217 IF YO>1 THEN YI=Y0O10C(37- FN LGT(YO)):ELSE Y11/YO*10^(37+ FN LGT(YO))1220 FACTOR=-LOG(Y1)1225 REM START OF l4AIN LOOP1230 FACTOR:FACTOR+LOG(YI)*21235 Y1=1/Y11240 IF NO=O THEN Y2=Y1:ELSE Y2=O1245 REM START OF INNER LOOP1250 NO:NO+11255 YI=YO/NO*Y11260 Y2=Y2+Y11265 IF(NO<(N-1)) AND(Y2<LIMIT) GOTO 12451270 ANSWER=ANSWER+EXP(LOG(Y2)+FACTOR-YO)1275 IF NO<(N-1) GOTO 12251276 IF Y1>O THEN RATIO=EXP(LOG(ANSWER)+YO-FACTOR-LOG(YI))
.... 1278 Y2=ANSWER1280 RETURN1290 REM ********************************* ******* ******u*******1320 REM START OF MAIN ROUTINE TO CALCULATE THRESHOLD (YO) FROM N AND PFA1330 YO=-I*LOG(PFA)
po, 1335 RATIO=1.01340 IF N<=1 THEN 14101350 REM First estimate for YO1360 YO=(SQR(-LOG(PFA))+SQR(N)-1)*SQR(-LOG(PFA))+N-SQR(N)1370 GOSUB 12011380 DO=LOG(Y21PFA)ORATIO1390 YO=YO+DO
1400 IF ABS(DO/Y0)=>3.0E-7 THEN 13701410 REM YO IS THRESHOLD FOR FIXED THRESHOLD DETECTOR1420 RETURN1425 REM**
17
IA .Y-.
Calculation of Pd for Marcum, Swerling and Weinstock Targets
1425 REP *RuiJJJ6.JaJJJ*JJJelNJo0JJJJI~gJuo**uJa*J *..J.J,***lJJulll*1430 REM CALCULATE Pd FROP S/N (X dB),CHI-SQUABE PARAMI'E? (K),h AhD YO1440 ELIMIT=1/(10*N):Y2=PFA
1443 YI=PFA/RATIO1444 NO=N1450 X=10(X/10)1460 S1=Y21470 XI=(K/(K+N*X))^K1480 X2=Xl1490 X3=X*N/(K+N*X)
. 1500 D1=K-11510 M=11520 R1=01525 IF X2=0 THEN GOSUB 1(611526 REM RESUME AF1ER UNDERFLOW LIMIT REACHED1530 L1=R11540 YI=YI/NO0Y1550 Y2=Y2+Y11560 S1=S1+Y1*(1-X2)1570 E1=(1-X2)0(1-Y2)1580 RI=S1+El
5" 1590 XI=(DI+M)/MIX1SX31600 X2=X2+XI1605 IF(X2>1) THEN X2=11610 M=M+11620 NO=N0+11630 IF ABS(1-LI/RI):>3.OE-7 THEN 15301640 IF EI=>ELIMIT THEN 15301650 REM RI IS THE PROBABILITY OF DETECTION1655 RETURN1656 REM **** iS** ****** O6*I*S*******O********I*** **u*S*B***6** *1660 REM SUBROUTINE TO SCALE FOR UNDEEFLOW1661 X4=0:X5=K*(LOG(K)-LOG(K.N#X))1662 X6=LOG(X3)1663 REM JUMP HERE TILL LIMIT1664 Y1=Y1/NO*YO
, 1665 Y2=Y2+YI1666 S1=S1 1
,p 1667 X4=X4+X6 LOG(D1+M)-LOG(M)1668 XI=EXP(X5+X4)
4 1669 X2=X2 Xl1670 M=M+I1671 NO=NO+l1672 IF X2=O THEN GOTO 16631673 RETURN1675 REM ************lillilillliiilllillliliilii0llilliilllillli
18
AtNEX C
Calculation of' Required Signal-to-Noise (Do)
8000 REE """""""""eaa~so,.,au...
8001 REM routine to solve roots of' f(x)=Rl by secant method8002 REM ShdBn IS CURRENT ESTIPATE Ih dB OF' SIN REQUIRED FOR Pd =PROB
8003 DEF FN LGT'(X)=LOGCX)/LOG(10)80014 LN= FN LGT(N)8005 REP~8006 PROB=0.958007 PROBLIMIT=0.0000 18008 REM ITERATION WILL BE STOPPED WHEN SNdB3 =PROB +/- PROBLiMIT8010 REM FIRST ESTIMATE OF' REQUIRED S/N IS FIT OF SOLUTIONS FOR PD=O.338011 IF N<3 THEN SNdB3=1O.5924-8749014*LN8012 IF N>=3 THEN SNdB3=7.138.1.018/LN-5.353*LN8013 SNdB3=SNdB3+J.3430 FN LGT(PFA/1.OE-6)/ FN LGT(PFA)80114 REM SECANT METHOD SEEDED WITH 2 POINTS STRADDLING Pd=0.338015 SNdB1=SNdB3-1.0:X=SNdBl:GOSUB 1430:PROB1:R18020 SNdB2=SNdB3+1.O:X=SNdB2:GOSUB 1430:PROB2=R1:18025 REM8028 IF(PROP2=O) AND(PROB1=O) THEN SNdB3=SNdB3+O.25:GOTO 80158029 IF(PROB2=1) AND(PROB1=1) THEN SNdB3=SNdB3-O.25:GOTO 80158030 SLOPE: (SNdB2^-SNdB1 )/ (PROB2-PROB1)8035 TESTSLOPE=(PROB-PROB2) 'SLOPE8036 IF TESTSLOPE>3 THEN SNdB3=SNdB2+ FN LGT(TESTSLOPE):GOTO 8050
'2>8037 IF TESTSLOPE<-3 THEN SNdB3=SNdB2- FN LCT(-TESTSLOPE):GOTO 80508040O SNdB3=SNdB2.TESTSLOPE8050 X=SNdB3:GOSUB 1430:PROB3=R18055 REM SNdB3 IS CURRENT ESTIMATE OF' Do FOR Pd=100*PROB3 %
*8060 IF' ABS(PROB3-PROB)<PROBLIMIT THEN GOTO 81008070 SNdB1 =SNdB2 :PROB1 :PROB28080 SNdB2=SNdB3:PROB2=PROB38090 GOTO 80308100 PRINT "ITERATION STOPPED AT ";SNdB3;" dB ";100*PROB3;" %8110 RETURN9000 REM IObOB*OIOO*IOOO5SSOBOO*gjggg
19
A :EX D
4Calculation of Paint Probability for Non-fluctuating Targets
1425 REV *******************************************i****1430 REM *** PROBABLILTY OF DETECTION FOR FON-FLUCTUATING TARGEfS***1431 REV CALCUATIODi OF Pd AT Signal-to-Noise = X OB1432 REV Probability of False Alarm : PFA1433 REM N Pulses Non-coherently IntegrFted1444 REM Fixed Threshold : YO1445 REh1440 Y2=PFA1443 Y1=PFA/RATIO1444 NO=N1450 X=10^(X/10)1460 S1=Y21465 X3=N*X1470 X1EXP(-X3)1480 X2=Xl
1492 X6:LOG(X3)1510 M=11520 R1=01525 REM TEST FOR UNDERFLOW CONDITION1526 IF X2=0 THEN GOSUB 16611530 L1=R11540 Y1=Y1/N0*Y01550 Y2=Y2+Y11560 S1:S1+Y1*(1-X2)1570 E1:(1-X2)*(1-Y2)1580 Rl=S1.E11590 X1=X3/M*X11600 X2=X2+Xl1610 M=M+I1620 N0:N0+11630 IF ABS(1-L1/R1)=>3.0E-7 THEN 15301640 IF E1=>0.001 THEN 15301650 REM RI IS THE PROBABILITY OF DETECTION1655 RETURN1656 RE **
-~ 1660 REM USE SCALING IiUTINE WHILE UNDERFLOW CONDITION EXISTS1661 X4=01662 X6=LOG(X3)1663 REM JUMP HER TILL LIMIT1664 Y1=Y1/N0*Y0
1665 Y2=Y2+Y1• .*' 1666 S=S+Y1
1667 X4:X4+X6-LOG(M)1668 X1:EXP(X4-X3)1669 X2=X2+Xl1670 M=M+11671 NO=NO1672 IF X2=0 THEN GOTO 16631673 RETURN1674 REM **************************************************************
7.1 - - WT~,-~-
20
fF x E
'ain Prograr~ for ContourVCD calculations.
1 REM DEFINE FUNCTIONS REUIRED FOR GEOMETRY ROUTINES*6 DEF FN LGT(X)=O.43t29i44*LCG(X)*7 DEF FN ASN(X)=ATN(X/SQR(1-X^2))
9 DEF FN GR(X)=2*Al* EN ASN(SQR(((X^2-(HH2-FiHl1Y>)/(J4*(AlHH1l)*CAl+HH2)))12 DEF FN EL(Xll= FN AS(2A*H2H1+H^-H12X2/2(lHl*)13 DEF FN INI'(XI'= FI ASN((2'A1'HH1+HH1^2+X^2)/(2'Al+HH1)'X))
2190 REY VCL ALGORITHN IS ITERATIVE OR R^i4 SCALING ( I OR S)2196 REP 30 MULTIPATH LOBES CALCULATED USING DEFAULT PARAYMETF;RS (POINTS%=302199 REMP***g***#**Ia*.u*,ae#*ga**,#***.2200 REM START OF !hAIN PROGRA'2201 R7=SQR(2*A1/M1)'(SQR(H1))2202 EINELEV=-1.0* FN ASN(Hl/7+R7/2/Al):M!AXELEV=TILT.1.1*B12203 PRINT"MIN ELEVATION =";57.3#NINELEV;"1 DEGREES"22014 DBLlNIT=O.25:REV. 0.25 dB LESOLUT]ON FOR ITERATIVE: ALGORITHM2205 PRINT"CALCS CAhRIED OUT TO n;57.3*MAXELEV;" DEGREES"2206 INCELEV=0.1' FN ASN(W/(2*H1))2207 ELTHETA(1)=0.7 0*INE:LEV2208 PRINT"USING LOOKUP TABLE PROVILEr,WHAT IS THE SIGNAL-TO-NOISE RATIO"2209 PRINT"REQLJIRED FOR THIS RADAR'S 'JCD CONTOUR":INPUT THRESH2210 LINP1=10^(Pl/1O)2211 QTHRESH=10 (-THRESH/40) :R0=R0'QThRESH2212 FOR I=1 TO POINTS%2213 FIRSTSLANT=ABS(RO'Fl0 (l+Rl'F2/Fl))22141 IF 1=1 THEN GOTO 22202215 ELTHETA(I)=ELTHETA(I-1)+INCELEV2216 IF ELTHETA(I)>FMAXELEV THEN I=POINTS% :GOTO 21400
*2220 THETA=ELTHETA(I):GOSUB 9202225 REN First estimate of range2227 SLANT=FIRSTSLANT22410 PRINT" FIRST SLANT ";SLANT22142 LOWLIMIT=1022415 ITERATION=02250 REM ark** Compute first estimate of altitude2251 IF ALG$="I" GOTO 2255
*2252 IF ITERATI0N=2 GOTO 23752255 HH1=HlM2257 H9(I)=SLANT*2+2ISLANT*(Al+HH1)ISIN(ELTHETA(I))+(Al+HH1)*22258 H9(I)=M1'(SQR(H9(I))-A1)2260 PRINT"HEIGHT =";H9(I);" FEET"2261 HH1=H1Mj:HH2=H9(1)/M1:G(I)= FN GR(SLANT)2262 H2=H9(I)2263 G8=G(I)2265 ITERATI0N=ITERATION+l2270 R7=SQR(2'Al/Ml)'(SQP(Hl).SQR(H9(I)))2280 REM Compute target multipath geometry
2290 GOSUB 26802300 REY, Comput~e (!]utter return for- ith point -C7(I)
2310 GOSUE 31400V'2320 REM Calculatiori/inter-polation of pattern propagation factor -F(I)
2330 GOSUB 247023140 REM radar, equaticn2350 F(I)=K6+F(I)+RCS-400 FN LGT(SLANT)-2#L3*SLANT
21
F ,ri prcgrar (cornt'd)
2352 NOISE=10* FN LI(LTNP1+(10^(C7(I)/10)))2353 INCSLAI*T=SLA NT-CLD.'4JANT23514 OLDEXCESS=EXCESS: 0LDSLANiT=,$LANT2355 EXCESS=F(I)-NGISE:IF ABS(EXCEFSS-THPiSH)<DBL)3-IT THEN COTO 23752356 INCEXCESS=EXCESS-OLDiYC.-lS2357 IF,(AES(EXCE.)S-THRESH) >ABS'(L0'LIK[IT)) TH-EN GOTO 23592358 LOWLl~IT=EXCESS-TFFESE:LOWG=G(I) :LCWR=OLDSLANT:LOWH=H9(I) :LOWP=F(I)2359 IF ITERATION<10 THEN GOTO 23652360 EXCESS=LWLI!IT+THRESti-:G(I) =L0WG:0LDS-LANT=L0WF:H9(I)=ILOWH:F'(I)=LOWPT2361 GOTO 2375:REM END ITERATION AND USE SMALLFS'r EXCESS IN VCD2362 IF, lTERATION<2 THEN SLANT=SLANT'QTHBESH'(10^(EXCESS/40))2363 IF ITERATION<2 THEN GOICO 23692365 IF ITERATION<4 THEN SLANT=SLANT*(QT1RESH*(10^(EXCESS/40)) )^052366 IF ITERATIONv(4 THEN GOTO 23692367 SLANT=SLANT+(THRESH-EXCESS)INCSL.NI/INCEXCESS2368 IF SLANT(0 THEN SLAh)T=2*R0'F.ND(1)+0.0811*W5
*2369 PRINT"SLANT= ";0LDSLANT;" ELEV= ";57.3'ELTHFTA(I);"' EXCESS= ";EXCESS;2370 PRINT:GOTO 22502375 RSLANT(I)=OLDSLANT2380 REM' Printout2390 GOSUB 28402395 IMAX=I21400 NEXT I21450 REM **I#***************#****i*f**O Oi
ER //[I
N.I/ /
.9<. /0//
4.)
N=100N=I
CL
-to o5 0 1 5 2 2 0 3
/1nltoNig lFigu / 1.//~it f cn o wriNcmI-i n
//1 lutatn tagt.P/1 .M I ~ladNI
23
Sw.lrh Case
' \
, - ,. 2..
o"\ \
t t,I N'
'\\
Nunbw of Pulses Integrated
'S.
4Figure 2. Signal-to-noise required for 50% paint probability.PFA = 0.000001. Swrling case [-IV targets.
U Swwlinq camG
ii
Ex
,\ \@ i'
\\ '
. ,, \
U,-"" III IV \
00
Nubr ofPleoneme
Figre 3. Signal-to-nois required for 95% paint PrctxPFA =0.000001. Swerling camQ I-IV t
q 25
TARGET
ANTENNA /
G2-
DIFATO
REI/
4/
Fiqx 4.Multpat geoetr wit sybolscisusedin ext
26
. . . . -77 -o
---- - -7 -7 -
- ~~.-"*..r. ~ 7 - -4-W-!- ---- -
*- -7.:: n-n7J.-- - ne - - nf- -.-
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5b10 1500 5
Range (n.niiles)
-~F Figumo 5. VQZtical coverage diagrami for UHF radar.Sea etate : 0Number of pulses integrated 1 75
* Target i I m'2. Swrling case IZrey scuas 1 4
.1 77 - - 4 ~ -''~- -
27
"4
'
f"4, P>2
-4.
4,,
* ---------- 4--4-$---*-------------
.._ .... ..l
#4444 + -- 44+4 4++#4 - 44 -- -- - -"4-_- -4 4 4 4 4 4 4 4 - 4 ..4- -1 4 *-
__. -444- ... . . ...
- .. .4 .. "
J -~ ~444.- 44 --- 444+- P+4 t
, Rangje (n.mils
l FigurQ 8. V~rtico31 coverage diagjram for UHF radar.; Sea state 1 6
.. 4Numb4r of pul-- int-egrate .. 'r
"' Target : I m'2. Swerling casa r,%0 Grey males 1 4
-- 444444'44444444-44P44~44- 444-
1~ v ' 77 R. I .T. X7 -7 I** * -V"I1 .7
28
CU
MO.
"it
OTq
4. 30=Ran;r 4:n1 )
Rargy samiles
*~~~W W. T... - r. err- r c
29
..... ....
Inq
..... .......... .....
.- L7
lossesi u ...
C)
U) 5 1..15 20 2..3
L-i RangeC n.miles)
7 Fi uro 8. Vertical roverroge eliwra for- S-barc! rc~or.
Niu~ix~ -f pulsv , integrated 1 5%A icir~jet 1 -n^2. SipliN~ cCsip
Gr~y GccalQG a
30
7.35
7.0
N free space behaviour
S-. .obe maximj
- j" receiver noise,- R-
.1.
10. ima
Rag nI I
ISO ... .. . . . . * t- " + - 4 - * . .. .. -. " .. .I. . ..* - - o ... ...- . ..,.- 10 1003X
"-"' Range ( n..mlle ).1
Figure 9. Signal returns for UIF radar at conetant elevation angleof 7. 0 aid 7. 35 grm. So etate 0.
131
X'
" N
.. 0
R "I
oF 7. and 7. rmSo ett
:" !clutter
".r,
II to too 0
~Fi1re 10. Sinl returns ICot UHF radar at ccnstant Qiation angle€ o 7.0 ondt 7.35 degrees Sea stt 6.
';:L o + . . .. . . . .. . . . . . . . . . . . . . . . . I 4 . . . . . . . . . . . . . . . .. l o o %
32
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33
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'7 ""' " ~ "--5*
4..s ,7 -
• .... / ," ../ .. 7 ' €'., o i;" .° -' " " l 7 ''.. .. , '/' ,'-. - , - ..~ .... ...
" -- 4 .- ... ...
( i . 5:: --- . : 4..; .. . ...-.... _. . .. "
4.-.,, "- i- ' .. " .... " .....
Rang~e ( n mile )
'4 Figure ,2 Contour VCD3 for UHF ridor.
. Sil state a 6* ~Si!-na1,-to-niee, 0 d (.+ 0.25
lgortIth. , Ite-ative
. r C-:..-.:..:i- .. . .314
M..r -//
.IT
;7 ,. /-171
f/ff
. . '" . / 1
i/ ..
Figure / /
Con' " ,t /U
a
, /fa, /.,* / . / ,
• ,..-/ / /" -/ • )
-. .- . ,. ' ' / / •/ /
ea t , 3r':j/K . " / """/, / , /
U)l / / // / / ' /7 • -
/../ /, .. ..
- ,, ,, , " . /7
:i na -o -o : 0. . dB 0 .2 5) - - .- / .
Ar /
-/77 . " ,. . . '
/ 1/-.o ,' -af".
0 + . , ,, --,
. .. ..- .-
Fi u 3. C nt u .....fo ..H .ra a........"-, Sea state:.
Sina-t-ojG. 0d (.. 0.25)...I;,.-.....A_. gou-ithm 2 ..:::at-.-
35
PT/
Rag . miles
Fiur 14. Cotur1fo H rdr
Se stat /
0inlt-os 0 d
Algorithm~ i Scaling<
....a ..............................* 36
IT.
4.)
C7 I
17
7,/,/ 7
4 1 A -
/ .." ; . .-- ." ... .!
* - -- :. .- .,..
0 20 40 60 80 t10 1 140 150
Range ( n mi les )
Figure 15. Contour VCD for UHF radar.Sea state 1 5Signal-to-noise s 0 c
* Algorithm : Scaling
* 37
CD
977
Si~na-to-oiso -. d
Algorithm; /c i
j-7 . W
38
E T4
C3 +
0// 10 is 2
! _//! '/, 6<4/' ,-,.,
Alorth i "Saling
I ", - ,
.- ---. -. . .
- .
0 + I I"" I . " .-. "
10 15
') Rang (# ;5. les
~iur 1. onor CDfo "-bn r4ada (low " flgl" .. E
Soc, state :.-"*""" 3;" "" "
* Signal-to-.oi.- .C "AloihI:Saii
0 39
1 ~ Y
/
/
/7
I -.
4-9
-~ -- ->
/
/
//
/
FigurQ 18. Reference axis syst2ms For discussion oF ship motion.
410
I'X.
Ile, --- ---
Rang . /i lea/~//
Figure~~,1 /9 Siuato ofteefc/fvriganen itfrL aa
/e state 3'
Sinl/onos s-.d
Anten/ tilt, :' Radmbten-0 n/ +1%o ~tba i
Alorth t /S/aling
* * .* *
44
.~4. IT '
~Z4i
~q.. ///
+/
Rag n.p *i As! I
Figum~~~~~~~~~~~ 26'iuaino feto ayigatnahih o H aa
Se state 1 3
SinlIonos 1~ > 0~/ MiAntnnaheihtlucuaton t 2 .5Z of noia/hih
42
S.[ DI s Bu TI ON COPY NO,
Chief Defence Scientist 1
Deputy Chief Defence Scientist 2
CERPAS 3
SSPA 4
JIO (DSTI) 5
RANRL Library master copy 6
Counsellor, Defence Science, Washington 7
Defence Science Rep. London 8
Librarian Technical Reports Centre, 9Defence Central Library, Campbell Park
OIC Document Exchange Centre DISB 10 - 27
Flag Officer Commanding H.M. Australian Fleet 28
, - Director General, Naval Operational Requirements 29
Director of Tactics, AIO and Navigation 30
4-S Director of Operational Analysis - Navy 31
Director of Surface and Air Weapons - Navy 32
Director of Electronic Warfare - Navy 33
Director of Radar Projects - Air Force 34
Director of Operational Analysis - Air Force 35
Director of Naval Aviation Policy 36
Director, Combat Data System Centre 37
Naval Scientific Adviser 38
Air Force Scientific Adviser 39
Officer-in-Charge RAN Trials and Assessing Unit 40
Director, RAN Tactical School 41
Joint Directors, Australian Joint Anti-Submarine School 42
Senior Librarian, Defence Research Centre Salisbury 43
Senior Librarian, Aeronautical Research Laboratories 44
Librarian H Block, Victoria Barracks, Melbourne 45
Dr M. F. Battaglia 46
Lt Cdr P. Williams, RAN 47
Dr J. L. Whitrow , Electronics Research Laboratory 48
RANRL Library 49 - 53
4'-
'.4
43
DOCUMENTI CONIrROL DATA Si1'YET
1. a. A.R. No. l.b. Establishment No. 2. Document Date 13. Task Nol
I I RANRL Tech Note I IA I 003-419 I (External) 1/84 May 1984 I A3/83 [
- I a. documcnt I 45The Calculation of the Radar I UNCLAF IVertical Coverage Diagram I b. title l7.No Refs I
UNCLAS I% c. abstract I 8
I UNCLAS I
8. Author(s) 9.Downgrading Instructions
"I BATTAGLIA, M.R. N/A
10. Corporate Author and Address Ill.Authority (as appropriate)ia.Sponsor b. Security
-.. RAN Research Laboratory c.Downgrading d.Approval°P.O. Box 706,
, Darlinghurst. N.S.W. 2010 a. NAV,"" b. HORD c.N/A (unclass)I.I d.M.D.Frost, Director RANRL
112. Secondary Distribution (of this document)I
I Im
I " Approved for Public Release
113. a. This document may be ANNOUNCED in catalogues and awareness servicesI available to :
I No limitations
113. b. Citation for other purposes (ie casual announcement) may be as for 13a.I
114. Descriptors O15. (OSATI Group
"I"Radar, model, multipath,clutter, 17090
I. .attenuation, backscatter,I,. probability of detection
F 116 Abstract -
I Algorithms are described for the calculation and plottingof radar vertical coverage diagrams. Two contour VCD algorithms are
I :.presented, with a brief discussion on the problem of numericalIo- stability, and the effects of ship motion and frequency agility.
4,
%
Aiis9 ir~ sun o f aa tcntn lvto nl
of7.and.35dgree. Saetta4
17igUr@ 17. rCont(
SQCI
All,
